Clavius, Christoph, Geometria practica

Table of contents

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[141.] PROBLEMA XXIV.
[142.] PROBLEMA XXV.
[143.] SCHOLIVM.
[144.] PROBLEMA XXVI.
[145.] PROBLEMA XXVII.
[146.] PROBLEMA XXVIII.
[147.] PROBLEMA XXIX.
[148.] PROBLEMA XXX.
[149.] PROBLEMA XXXI.
[150.] PROBLEMA XXXII.
[151.] PROBLEMA XXXIII.
[152.] PROBLEMA XXXIV.
[153.] PROBLEMA XXXV.
[154.] PROBLEMA XXXVI.
[155.] PROBLEMA XXXVII.
[156.] PROBLEMA XXXVIII.
[157.] PROBLEMA XXXIX.
[158.] ALITER.
[159.] ALITER.
[160.] PROBLEMA XL.
[161.] ALITER.
[162.] PROBLEMA XLI.
[163.] PROBLEMA XLII.
[164.] PROBLEMA XLIII.
[165.] PROBLEMA XLIV.
[166.] SCHOLIVM.
[167.] PROBLEMA XLV.
[168.] FINIS LIBRI TERTII.
[169.] GEOMETRIÆ PRACTICÆ LIBER QVARTVS.
[170.] AREAS
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            <s xml:id="echoid-s5352" xml:space="preserve">
              <pb o="137" file="167" n="167" rhead="LIBER TERTIVS."/>
            tudinem ex maiore deprehendimus. </s>
            <s xml:id="echoid-s5353" xml:space="preserve">Nam hic minor altitudo inquirenda eſt
              <lb/>
            CH, & </s>
            <s xml:id="echoid-s5354" xml:space="preserve">maior NG, ex cuius vertice N, terminum C, videri poſſe ſtatuimus.</s>
            <s xml:id="echoid-s5355" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5356" xml:space="preserve">DISTANTIAM inter pedes menſoris, & </s>
            <s xml:id="echoid-s5357" xml:space="preserve">ſignum aliquod in plano
              <lb/>
            Horizontis beneficio baculi metiri, quando extremus terminus di-
              <lb/>
            ſtantiæ videri poteſt.</s>
            <s xml:id="echoid-s5358" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div354" type="section" level="1" n="147">
          <head xml:id="echoid-head150" xml:space="preserve">PROBLEMA XXIX.</head>
          <p>
            <s xml:id="echoid-s5359" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5360" xml:space="preserve">
              <emph style="sc">Absolvtis</emph>
            dimenſionibus, quæ per quadrantem, & </s>
            <s xml:id="echoid-s5361" xml:space="preserve">quadratum ſieri
              <lb/>
            ſolent, libet nonnullas alias rationes dimetiendi a diungere, vt illis, quando ne-
              <lb/>
            que quadrans, neque quadratum adeſt, vti poſsimus. </s>
            <s xml:id="echoid-s5362" xml:space="preserve">Ex pluribus autem me-
              <lb/>
            dis illis ſolum ſeligemus, quo faciliorem vſum habent.</s>
            <s xml:id="echoid-s5363" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5364" xml:space="preserve">
              <emph style="sc">Sit</emph>
            ergo diſtantia metienda D B. </s>
            <s xml:id="echoid-s5365" xml:space="preserve">In
              <lb/>
              <figure xlink:label="fig-167-01" xlink:href="fig-167-01a" number="98">
                <image file="167-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/167-01"/>
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            D, erigatur baculus DE, minor altitudine
              <lb/>
            AC, ab oculo menſoris ad pedes, rectus
              <lb/>
            ad Horizontem. </s>
            <s xml:id="echoid-s5366" xml:space="preserve">quod fiet, ſi filum cum
              <lb/>
            perpendiculo baculo adhærebit, vella-
              <lb/>
            pillus ex E, demiſſus in punctum D, ca-
              <lb/>
            det. </s>
            <s xml:id="echoid-s5367" xml:space="preserve">Deinde retro cedat menſor vſque ad
              <lb/>
            A, donec radius viſualis ex C, prodiens,
              <lb/>
            & </s>
            <s xml:id="echoid-s5368" xml:space="preserve">per extremum E, baculitranſiens oc-
              <lb/>
            currat puncto B; </s>
            <s xml:id="echoid-s5369" xml:space="preserve">intelligaturque duci recta E F, ipſi A B, parallela. </s>
            <s xml:id="echoid-s5370" xml:space="preserve">Quoniam
              <lb/>
            igitur triangula C F E, E D B, æquiangula ſunt; </s>
            <s xml:id="echoid-s5371" xml:space="preserve">quodanguli F, D, ſintrecti, &</s>
            <s xml:id="echoid-s5372" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-167-01" xlink:href="note-167-01a" xml:space="preserve">29. primi.</note>
            ECF, BED, æquales, internus, & </s>
            <s xml:id="echoid-s5373" xml:space="preserve">externus, &</s>
            <s xml:id="echoid-s5374" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5375" xml:space="preserve"> Siigitur fiat.</s>
            <s xml:id="echoid-s5376" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-167-02" xlink:href="note-167-02a" xml:space="preserve">4. ſexti.</note>
              <note style="it" position="right" xlink:label="note-167-03" xlink:href="note-167-03a" xml:space="preserve">
                <lb/>
              Vt CF, differentia inter ba- \\ culum D E, & menſoris ſta- \\ tur am AC. # ad FE, ſpatium inter \\ menſerem & baculum: # Ita E D, lon- \\ gitudo bacu- \\ linoti. # ad D B,
                <lb/>
              </note>
            nota prodibit diſtantia quæſita D B, in partibus baculi D E, vel ſtaturæ menſoris
              <unsure/>
              <lb/>
            AC. </s>
            <s xml:id="echoid-s5377" xml:space="preserve">Debent enim baculus, & </s>
            <s xml:id="echoid-s5378" xml:space="preserve">ſtatura menſoris per vnam eandemque menſu-
              <lb/>
            ram eſſe cognita.</s>
            <s xml:id="echoid-s5379" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5380" xml:space="preserve">ALTITVDINEM turris, aut alterius rei per baculum indagare.</s>
            <s xml:id="echoid-s5381" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head151" xml:space="preserve">PROBLEMA XXX.</head>
          <p>
            <s xml:id="echoid-s5382" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5383" xml:space="preserve">
              <emph style="sc">Sit</emph>
            in figura præcedentis problematis metienda altitudo A C. </s>
            <s xml:id="echoid-s5384" xml:space="preserve">Figatur
              <lb/>
            in terra baculus G H, rectus ad Horizontem, & </s>
            <s xml:id="echoid-s5385" xml:space="preserve">aliquãtulum maior ſtatura mẽ-
              <lb/>
            ſoris ab oculo ad pedes quæ ſit IK. </s>
            <s xml:id="echoid-s5386" xml:space="preserve">Deinderetro cedat menſor vſque ad I, ita vt
              <lb/>
            eius oculus in K, conſtitutus faſtigium C, inſpiciat: </s>
            <s xml:id="echoid-s5387" xml:space="preserve">intelligatur que ducta recta
              <lb/>
              <note symbol="c" position="right" xlink:label="note-167-04" xlink:href="note-167-04a" xml:space="preserve">coroll. 4.
                <lb/>
              ſexti.</note>
            KL, Horizonti AB, parallela, ſecans baculumin M. </s>
            <s xml:id="echoid-s5388" xml:space="preserve"> Quoniam igitur triangu- la KMH, KLC, ſimilia ſunt, propter parallelas M H, L C: </s>
            <s xml:id="echoid-s5389" xml:space="preserve">ſi </s>
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